Winger Rodriguez has been compared to Cristiano Ronaldo after impressing with Real's B team, but has toiled to earn promotion to the senior squad under Jose Mourinho.
The 19-year-old has netted 23 goals in 63 matches for Real Madrid B over the past two years, but is prepared to leave the Bernabeu to enhance his future prospects.
Tottenham and Manchester United have been linked with the teenager, who is valued at £30 million by Real.
“There are many good players in the first team but right now all of us in the academy see it as being a long way off,” said Rodriguez.
“I don't know what's going on there, but Mourinho is picking players from the first team more, which is normal, but I think that the academy is working well too.
“Why have I not been given a chance? I don't understand it. I keep on working hard, but I don't know. I'm thinking about my team now and myself, that's the priority.
He continued: “I'm going to keep on working hard there and I hope the club knows I'm working hard, I'm sure they do know and they will be watching.
“I believe I have earned the opportunity, too. But if the opportunities don't come, you lose hope. I dream of playing for Real Madrid yes, but I'm gradually losing hope, when I see the opportunities aren't coming my way.”
“Would I leave? Yes, I am just contracted until 2014. If I fail to get a chance then I will look at other things. I want to play for Real Madrid, but if they do not trust me here, perhaps other teams will.
“Have I had a contract offer? No, I have had no offer from the club. I guess I will be waiting. My agent is considering other options and we will wait. There is still time.”